Why does reducing Resolution X increase my camera's FOV and increasing it reduce FOV?
In short
If you set Focal Lenght and Sensor Size values matching your real-cam ... it should work. Those two values represent perspective (optics) behaviour, including FOV (sure without lens distortions and other optics defects). Dimension values (Resolution X/Y in px) are as naming states - about rendered dimension, that can be set as cropped or extended result over sensor FOV.

Closer
You have to stop think about render Dimension / Resolution parameters as something that represents real camera FOV. X/Y values here relates to sensor size only in sense of max Width or Height. The rest of format is &quot;cropped&quot; or &quot;extended&quot; over sensor FOV.
To limit rendered format to one of the real-cam sensor size (width / height) you have to choose under Camera Properties &gt; Camera &gt; Sensor Fit &gt;  Horizontal or Vertical. Don't use Auto, this use squared size of sensor.

If you want to stay in range of real camera for example Sony A7S

go to Camera Properties &gt; Camera &gt; Sensor Fit, switch from Auto  to Horizontal or Vertical and set Sensor Size to 35.8 x 23.9 mm
go to Camera Properties &gt; Lens and set appropriate Focal Length (here 35 mm)

These two parameters mimic your real cam. To see what real camera see (real FOV) enabled under Viewport Display &gt; Sensor

Dashed rectangle is Sensor size, green square is Camera object in size 1920x1080 px when Sensor Fit &gt; Horizontal. From that you can see that your sensor is able to capture movie file in 1920 x 1280 px (1.5 proportion).
Anymway with this setup blender camera should mimic real-cam FOV.
By changing X or Y values under Output Properties &gt; Dimension &gt; Resolution you can see only FOV-width is changing when Sensor Fit is set to Vertical or FOV-Height is changing when Sensor Fit is set to Horizontal.

So what is changing here is not Camera Field of View (FOV), but only resolution and aspect of rendered image.
I was always asking my self why this Dimension &gt; Resolution is not a part of camera properties ... and here it is - they are two separate things. It looks confusing just because changing Output &gt; Resolution is changing shape of Camera object in 3D view. That gives an impression I'm changing camera itself, but in reality it is more like you are cutting printed image by scissors or adding more canvas on sides, because sensor and all the optics is still the same unchanged in camera properties.
Any advanced explanation is welcomed, so in mean time ... I hope this helps a bit.
Also for more convenient work to match other real-cam setups try Real Camera addon.


Bug report – Viewport Display &gt; Sensor enabled is working under 2.83, but not for any 2.9x. Since it is just for
reference it should not affect result, but make it hard to illustrate
for you what is real-cam FOV. I'm going to check if someone posted a
bug report.*